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Thursday, June 28, 2007

Yesterday I picked up my son's report card. He was rated "above standard" in math and science (of course! Kindergarten, and we completed the 1st grade in math already at home! Russian math, not a fuzzy one). OK, but he was placed in class 105 for the next year.

Let me explain a little. I work in middle school - and I hate heterogeneous placement... I tried to ensure that my honor classes are as homogeneous as possible. Honor classes in each grade are numbered 01.

So today I went to my son's school to clarify the issue: do they track? What is 05 class? Can I place him in class with accelerated math (if they have it)?

The answers were (and since they know that I am a teacher "from across the street" they were a little more clear than a moment before on the phone obviously answering a similar question):

-District demands heterogeneous placement - we follow. There are no difference between the classes by number.-well, we don't know who is the teacher in that class for sure (that's true, nobody knows anything for sure in the schools until September!)-if he is recommended by his teacher he will be pulled out for enriched math no matter what class he is in

After I left the office, the secretary ran after me:-She just looked up and found that 105 is an inclusion (CTT) class! So my son was placed there for good balance and this is fair to other students and teachers! (Sure, I know inclusion classes! He will be there to help the teacher teach slower students instead of LEARNING himself. And that "fair" talk drives me nuts - I heard it in my school from the teachers, too. I don't see too much good in heterogeneous placement, sorry. Especially, when it concerns my child. And I don't care if it's fair for other children. Life is a competition after all).

-Well, she understands... but she can't advise anything. If I have any other reservations, I shall feel free...

Now, Add to that Everyday Math curriculum and Balanced Literacy with Social Studies focused on the "Neighborhood" - I will start my search again. The worst - most public schools (all as I was told) use EM in Brooklyn, and I am restricted by many things such as who and how drops him off, picks him up from school etc. Oh... And I planned to relax this summer!

Now that the Supreme Court has ruled against race-based student assignment plans (within parameters set by Justice Kennedy, I gather), I wish to heck we could get our policy wonks & columnists to stop writing race-based columns and policy briefs.

But all too often the continual association of "badness" with "blackness" and "Hispanicness" does the opposite.

It's not that policy wonks and columnists should be color-blind. What's good about NCLB - one of the things - is that it forces affluent school districts like mine to disaggregate their data, to tell taxpayers & parents how well their disadvantaged kids are doing.

The problem with making race the focus is that you factor out curriculum, pedagogy, teacher training, and even education case law and accountability as essential components of analysis. Once you do that, you limit your ability to understand what's going on inside our schools.

I don't understand what's going on inside our schools, either, but I've come to feel that there's a great deal more - or less - than the Washington consensus suspects or even imagines.

Reformers in the nation’s capital agreed on ....the nature of the education problem....How did the NCLB advocates understand the problem they intended to solve? First and foremost, they were concerned about the nation’s “achievement gap”--primarily the disparity between the performance of white and Asian students on the one hand, and African-American and Latino students on the other. In 2000, the typical African-American 12th grader was reading and performing math at approximately the same level as the average white 8th grader. Leaders of both parties declared this to be unacceptable, a violation of equal opportunity, and a threat to America’s future competitiveness (Thernstrom and Thernstrom, 2003).

I'm convinced that "the nature of the education problem" isn't the achievement gap.

The achievement gap is a scandal; it needs to be narrowed and/or closed and/or reversed, depending upon the child.

But the achievement gap isn't the problem. It's the symptom of the problem, or so I will believe until sound value-added analysis shows me I'm wrong.

In light of all this, my guess is that paying "effective teachers" lots more money to teach in urban schools won't narrow the gap appreciably, though I assume it would help.

This is an example of the "perception gap" between people with kids in the schools and analysts without kids (currently) in the schools. Pundits and policy analysts read the new report on teacher equity from Tennessee(pdf file; eduwonk link) as proof that teacher equity is a major problem and, thus, a major solution, if we could just take all the good teachers away from the white kids and give them to the black kids.

Sometimes you have to wonder: are analysts thinking about the real world at all? If urban parents didn't like busing, just how receptive are urban parents of any race or ethnicity going to be to a top-down scheme to strip their children's schools of the best teachers?

While the TN study does show that low poverty/low minority schools have better teachers than high poverty/high minority schools, I suspect the figures are far less dramatic than members of the general public would expect:

It's possible that a 3-point difference is much larger than it appears "on paper," of course. And the report does say that the "most effective" teachers in high poverty schools aren't as effective as the "most effective" teachers in low poverty schools.

But this passage makes me wonder:

A teacher effect score below zero indicates that the average student in the teacher’s class made less growth than the statewide average, while a teacher effect score above zero indicates that the average student in the teacher’s class made more growth than the statewide average.

[snip]

If a teacher’s effect score was below zero, and one standard error above the score was still negative, the teacher was categorized as “least effective.”

If a teacher’s effect score was positive, and one standard error below the score was still positive, the teacher was categorized as “most effective”.

As usual, I wish I'd been able to take a statistics course by now..... but lacking the requisite background knowledge, my question is: if we're comparing "most effective" teachers in high poverty schools to "most effective" teachers in low poverty schools on the criteria of their students beating the statewide average ---- aren't we potentially saying that the "most effective" teachers in the high poverty schools are actually better than the "most effective" teachers in the low poverty schools?

Wouldn't it be more of an achievement to have your high-poverty students beating the statewide average than to have your low-poverty students beating the statewide average?

Or have I got the logic completely wrong? [see Doug's answer, below]

The figures on "least effective" teachers are also much closer than we non-pundits would assume:

High poverty/high minority schools: 16% of the teaching staff is "least effective"Low poverty/low minority schools: 23.8% of the teaching staff is "least effective"

I suspect most middle and upper-middle class parents would be horrified to learn that students in classes taught by 16% of the teachers in their schools are ending up performing more than 1 standard deviation below the statewide average.

That 16% figure, btw, jibes with the figure Ed was always cited when he headed the California History Social Science Project. Administrators and teachers universally told him that 15% of teachers were terrible.

Here's another interesting passage:

Although many of the beginning teachers in high poverty/high minority schools are among the state’s most effective, many of them do not stay in these schools or lose their effectiveness over time.

There are more "most effective" beginning teachers in high poverty/high minority schools (roughly 17%) than in low poverty/low minority schools (roughly 12%).

So.....looking at this, and I realize it's dangerous to make comparisons across time.... what I see happening is that high poverty schools start out with 17.6% of their novice teachers being "most effective"; 10 years later that figure stands at 16%.

Low poverty/low minority schools in TN start out with 12% "most effective" novices; 10 years later that figure is up to 27%.

trouble in River City

This is bad news, because the baby boom teachers are retiring and being replaced by novices.

I've been reliably told that 10 years ago my district didn't hire novice teachers; we didn't even interview novice teachers.

Now all of our hires have no more than 5 years teaching experience as far as I've been able to determine. (This may not be the case for SPED teachers.)

People tell me this is happening all over the country. Given the pension situation in many communities, I assume that's the case.

If the Tennessee figures hold true for other schools, my own school district may be looking at a reduction of a teacher quality from 27% of teachers being "most effective" to as low as 12%.

update from Doug:

"Or have I got the logic completely wrong?"

Not completely. 8-)

First, by the description, the students skills aren't being compared to the average, their progress is being compared to the average. On the face of things, this seems reasonably fair. A good teacher should be able to create more progress in his students than a poor teacher. This seems to be a measure of that.

Second, the dividing line is not teachers whose progressed more than a standard deviation below the average, but students whose progress was more than one standard error below the average. With a large population of teachers, this would seem to be a very small difference.

In fact, this would result in any teacher whose classes learned detectably better than average being rated as "most effective". Talk about your low expectations!

What this says to me is that the difference between the top 20% of teachers and the mean is barely detectable. In other words, this would imply that there is little benefit to most teachers, since more than 60% of teachers are statistically indistinguishable.

Perhaps the top 10% (or 5%, or 1%) is actually capable of making a significant difference in learning, but that can't be determined from what you report.

I find that both surprising and discouraging. All I can hope is that either I made a mistake in analysis or the survey has some problem.

I was reading the Glenn Commission report, published almost seven years ago, and was struck with how things haven’t changed-- at least not for the better anyway. It’s probably not an exaggeration to say that the state of math and science education has actually have gotten much worse. I rambled on about it a bit here.

As I read the report I came across a reference to “reasoned discovery” and had to pause and attempt to understand what the authors meant by this term. I got this nagging feeling that they didn't mean it in the constructivist definition of "discovery" per se.

This term only appears once in the entire report in this particular passage:

In Japan, by contrast, closely supervised, collaborative work among students is the norm. Teachers begin by presenting students with a mathematics problem employing principles they have not yet learned. They then work alone or in small groups to devise a solution. After a few minutes, students are called on to present their answers; the whole class works through the problems and solutions, uncovering the related mathematical concepts and reasoning. The students learn through reasoned discovery, not lecture alone.

The first thing I did was google “reasoned discovery” assuming I’d find so many articles that I’d have to do some serious sifting. That’s not what happened at all. I found some references to reasoned discovery in some scientific articles and research but I struggled to find a clear definition of it as a type of discovery.

So why the adjective, "reasoned"?

I don’t believe “discovery” in the implementation carried out by most proponents of constructivism is what the Glenn Commission authors were referring to when they articulated “reasoned discovery”. I think that they had a very specific idea in mind and chose their words very carefully. In another passage they referred to “mathematics as the language of scientific reasoning” which suggests that they used the adjective “reasoned” to distinguish it from “discovery” in and of itself.

By dissecting the passage, I tried to come to a better understanding of what these 25 collaborators had in mind.

1. The collaborative work is closely supervised. The teacher plays an active role in the learning.2. The group presents the answer after only “a few minutes”. There is no prolonged “struggle”.3. Immediately thereafter, the whole class works through the problems and solutions presumably under the careful direction of a teacher “uncovering the related mathematical concepts and reasoning.”4. The students “learn through reasoned discovery, not lecture alone” which means that lecture (direct instruction) is a tandem component and is assumed to be part of the teaching/learning process.

After staying up and thinking about this for much too long, I'm still wondering what “reasoned discovery” means.

Wednesday, June 27, 2007

One problem with teaching mathematics in the K-12 system - and I see it as a major difficulty - is that there is virtually nothing the pupils learn that has a non-trivial application in today's world. The most a teacher can tell a student who enquires, entirely reasonably, "How is this useful?" is that almost all mathematics finds uses, in many cases important ones, and that what they learn in school leads on to mathematics that definitely is used.

Things change dramatically around the sophomore university level, when almost everything a student learns has significant applications.

I am not arguing that utility is the only or even the primary reason for teaching math. But the question of utility is a valid one that deserves an answer, and there really isn't a good one. For many school pupils, and often their parents, the lack of a good answer is enough to persuade them to give up on math and focus their efforts elsewhere.

mathematician in residence programs for 8-12

Another possibility to try to motivate K-12 students (actually, in my experience from visiting schools and talking with their teachers, it is the older pupils who are the ones more likely to require motivation, say grades 8 or 9 upward) is for professional mathematicians to visit schools. I know I am not the only mathematician who does this. There is nothing like presenting pupils with a living, breathing, professional mathematician who can provide a first-hand example of what mathematicians do in and for society.

I recently spent two weeks in Australia, as the Mathematician in Residence at St. Peters College in Adelaide. This was only the second time in my life that a high school had invited me to spend some time as a visitor, and the first time overseas - over a very large sea in fact! In both cases, the high school in question was private, and had secured private endowment funding to support such an activity. For two weeks, I spent each day in the school, giving classes. Many classes were one-offs, and I spent the time answering that "What do mathematicians do?" question. For some 11 and 12 grade classes, we met several times and I gave presentations and mini-lessons, answered questions, engaged in problem sessions, and generally got to know the students, and they me. You would have to ask the students what they got from my visit, but from my perspective (and that of the former head of mathematics at the school, David Martin, who organized my visit), they gained a lot. To appreciate a human activity such as mathematics, there is, after all, nothing that can match having a real-life practitioner on call for a couple of weeks.

Thought of on its own, such a program seems expensive. But viewed as a component of the entire mathematics education program at a school, the incremental cost of a "mathematician in residence" is small, though in the anti-educational and anti-science wasteland that is George Bush's America it may be a hard sell in the U.S. just now. But definitely worth a try when the educational climate improves, I think. If it fails, the funds can always be diverted elsewhere.

I often hear complaints funneled via their high school teachers that students who used graphing calculators while in high school as a means of supporting their understanding of calculus concepts find, when they get to college, that they are not allowed to use them.

We're buying them in bulk. The small flags(scroll down) are great, too. I've just used the small flags to mark lessons in Saxon Algebra 1/2 I want Christopher to do; I used the arrow flags to mark specific problems in the problem sets.

Now that I have small flags, arrow flags, and (soon) page markers, I may be able to find the passages I'm looking for in Stereotypic Animal Behaviour, a book in which the word "stereotypies" appears on each and every page, making each and every page seem like the exact same pageyou looked at moments before. World's worst index, too.

If I can find passages I'm looking for, I may be able to complete Chapter One of Temple's & my sequel to AIT.

That would be good.

Never let it be said there isn't a technological solution to a problem that is ruining your life.

In my experience, government departments use Powerpoint because they can then call what they are doing a "presentation" which means they don't have to go through all the procedural rules for documents (eg circulating them two weeks beforehand).

Powerpoint is wonderful if used properly. That means using it as something adjacent to a speech. A set of slides should not be a standalone document - if it is people are going to spend all their time reading the slides and not listening to your speech.

from Barry (who works for the EPA):

There are many documents other than PowerPoint that can ciruclate without going through procedural rules. But in the end, if someone files a Freedom of Information Act request about a particular subject, and wants ALL documentation related to it, PowerPoint presentations must be provided to comply with the request.

from Tracy again:

In NZ slides from presentations may be obtained under the Official Information Act (unless there's an extremely good reason why not). Indeed, officials have been required to write down their recollections of what was said at informal meetings and release that under NZ's Official Information Act.

I should pull the Dummies book. As I recall, he made Tracy's point about PowerPoint, which is that the slides are a distraction from the speaker. His purposes are different, obviously; Public Relations for Dummies explains how to give speeches as a means of drumming up business.

In that case you don't want anything distracting from the speaker.

iirc, he had a cool "If you want more information ask me for this green sheet" technique he recommended everyone use.

Sometime during the speech you tell people that if they want more information they should come up after the speech and ask for "the green sheet" (a green sheet of typing paper with material printed on it)..... at which point you capture their business card & contact info.

We were watching the first season of 24 last night, which is great because we can finally see why and how that show hooked so many people.

All we'd seen thus far were this season - awful! - and the 2nd season on DVD, which was better than this year's episodes but far from riveting. (We saw the second season on DVD before seeing the first season on DVD for reasons I will not go into on a blog, other than to say that the Chinese bootlegging industry seems to have a problem with labeling.)*

Anyway, as I say, we were watching the first season of 24 last night.

Midway through the episode, Dennis Haysbert & his wife are touring a Los Angeles school and the female principal says something like, "The problem with Los Angeles schools is the parents suck."

Haysbert nods sympathetically and the principal then whines -- I'm serious, she whines -- "What can the federal government do about parents?" at which point a bad guy appears and Haysbert seamlessly hands the principal off to his aide, Mike, who says he's been privileged to write the white paper on education for the Senator and is last heard muttering, "Parent involvement is very important."

Steve H left this demonstration (proof?) of why, when calculating slope, it's OK to use either point as "Point 1":

(y1-y2)/(x1-x2)

= -(y2-y1)/[-(x2-x1)]

= -1*(y2-y1)/[-1*(x2-x1)]

= -1/-1 * (y2-y1)/(x2-x1)

= (y2-y1)/(x2-x1)

Here's my question.

What are the justifications for each step?

(y1-y2)/(x1-x2)

= -(y2-y1)/[-(x2-x1)] mutiplicative identity ??

= -1*(y2-y1)/[-1*(x2-x1)] mutiplicative identity again??

= -1/-1 * (y2-y1)/(x2-x1) commutative property of multiplication??

= (y2-y1)/(x2-x1)

I'm definitely ready for something more formal...although I'm not sure where I'm going to find it.

Think I'll check Dolciani's & Foerster's books.

update from Steve:

I think schools should spend much more time on these identities. They should show how they are used in all sorts of interesting ways, forwards and backwards. I don't think I really learned algebra until this happened. [Catherine here: I agree absolutely. I'm really feeling a need for this, and it's not really something I can "provide" for myself - at least, not without a HUGE amount of effort.]

(y1-y2)/(x1-x2)

= -(y2-y1)/[-(x2-x1)]

This is the Distributive Law, in reverse, if you will.

[Catherine: I didn't see this! Now I do!]

= -1*(y2-y1)/[-1*(x2-x1)]

I suppose you could call this the Multiplicative Identity. I mentioned before that the sign "belongs" to the term that comes after it. I always like to think of a sign as a +1 or a -1. [Catherine: me, too]

= -1/-1 * (y2-y1)/(x2-x1)

I suppose you could call this the Commutative Property of Multiplication law. In other words, it doesn't matter which way you multiply fators. That's why I liked to have students circle the factors in a rational term. Then they know that they can move the factors to any position.

= (y2-y1)/(x2-x1)

I got rid of the -1/-1 using the Multiplicative Inverse law.

It's interesting that in the list of basic identities I found online that there wasn't an identity for

Geometry and trigonometry are integrated throughout the first 3 books.

So I'll spend next year working my way through Advanced Mathematics while Christopher, who will be in 8th grade, finishes Math A: algebra and some geometry. (Math A is still a 1 1/2 year course, as far as I can tell, though people keep saying NY is going back to the old algebra 1 - geometry - algebra 2 sequence. His class began Math A in January.)

Freshman year, if he stays on the fully accelerated track which I expect he will, he'll be taking geometry - real geometry, with proofs. Or so I hear. (Is this a separate, souped-up geometry course that's neither Math A nor Math B? Don't know! I get all my info from my neighbor, whose son is a year ahead in school.)

Assuming you aren't hopelessly confused by now,* you may see the problem.

He's catching me.

I'm 2/3 of the way through Saxon Algebra 2, and I have yet to do a proof. Unless there are a lot of proofs in Advanced Mathematics (which there may be - don't know)** I'm going to be starting geometry-with-proofs the same time Chris does.

Just checked the scope and sequence for Advanced Mathematics:ProofsElements of ProofsUnderstand basic logic and reasoningState the contrapositives of conditional statementsState the converses and inverses of conditionalstatementsDo proof outlinesDo formal proofsTheoremsProve the chord-tangent theoremProve theorems about secants and tangentsProve theorems about chord productsProve the Pythagorean theoremProve similarity of trianglesProve the law of sinesProve that equal angles imply proportional sides

re: Norwegian IQ study as future "proof" that peer-tutoring and heterogeneous grouping are really, really good for gifted children:

The sociobiological argument against heterogeneous grouping is that siblings share 25% common genes, and therefore have a biological stake in each other's success. This is not the case within a heterogenous peer group, where others would be viewed as a competitive threat to their survival.

The big news at dinner last night was that heroic Chris Benoit, having canceled an engagment on Saturday and rushed home to handle a "family emergency," was now dead, along with his wife and, Christian thought, her step-son from a previous marriage. (The details got mangled in translation.)

The spin seemed to be that the wife's ex-husband had slaughtered them all. Years ago the ex-, a writer for WWE, had created a storyline in which Chris Benoit stole his wife away from him; shortly thereafter Chris Benoit did steal the wife, or so I'm told.

And now everyone was dead.

A great tragedy, and WWE aired a 3-hour tribute to Benoit a few hours later. Little kids all across the country watched it, I'm sure.

...the 2.3 I.Q. points that differentiate the average Norwegian firstborn from the average Norwegian second-born in a two-child family is equivalent to the firstborn having a 13 percent greater chance of getting into a better college. This difference is also equivalent to the firstborn having 1.3 times the odds of getting into a better college, compared with the second-born.

It is also worth noting that 2.3 extra I.Q. points (the advantage enjoyed by a firstborn over an immediately younger sibling) is approximately equivalent to scoring an extra 15 points on each SAT test, or a combined 45 points on the three current tests, which have a mean combined score of about 1,500 points. The cutoffs for acceptance to the best colleges, based on SAT scores, often hinge on where one stands within a range of just 40 to 50 points on the three tests combined.

Seen in this perspective, these documented differences in I.Q. by birth order are hardly negligible. However, as I said in a recent interview published in part by Nature, if I had the choice of having 2.3 extra I.Q. points or having the “enlarged curiosity” that Charles Darwin’s uncle, Josiah Wedgwood, recognized in his nephew on the eve of Mr. Darwin’s departure on the Beagle to circumnavigate the globe, I would unhesitatingly choose the latter.

So, yes, I.Q. is hardly everything, and much that makes people successful in life has to do with how people use their intelligence rather than with their intelligence per se. In addition, there is considerable evidence suggesting that siblings born later use their intelligence differently from the way firstborns use theirs. Indeed, later-born siblings would appear to have 2.3 extra points of one difficult-to-measure intellectual skill, associated with unconventional thinking, that firstborns sometimes lack.

brace yourself

When I.Q. scores were adjusted to account for differences in maternal education, parental income and parental marital status, the difference in I.Q. scores between firstborns and only children was reduced to just 0.6 points.

This remaining difference does suggest that Robert Zajonc’s theory about older siblings teaching younger siblings may help to explain why firstborns have higher I.Q.s than only children, since only children have no one to teach. However, this I.Q. difference is also consistent with the theory of niche partitioning within the family. Only children do not compete with younger siblings for parental favor. Hence they are presumably less motivated than firstborns with younger siblings to nail down the niche of the family “achiever.”

The news reports of this study will be used to justify heterogeneous grouping and peer-tutoring.

So be prepared.

The counter is:

a) sibling tutoring was not mentioned in the study

b) sibling tutoring is simply Robert Zajonc's hypothesis as to why this study and so many others should find that firstborns have higher IQs

c) to my knowledge, no one has presented evidence that firstborns routinely tutor their younger siblings (I had 3 younger siblings & I didn't spend any time teaching them how to read or do arithmetic)

d) until someone does present evidence that older siblings spend enough time tutoring younger siblings to raise their own IQs (and until we have some evidence that sibling-tutoring does raise the tutor's IQ) niche partitioning should be the preferred explanation

In the study, Norwegian epidemiologists analyzed data on birth order, health status and I.Q. scores of 241,310 18- and 19-year-old men born from 1967 to 1976, using military records. After correcting for factors that may affect scores, including parents’ education level, maternal age at birth and family size, the researchers found that eldest children scored an average of 103.2, about 3 percent higher than second children (100.3) and 4 percent higher than thirdborns (99.0).

The difference was an average, meaning that it varied by family and showed up in most families but not all.

The scientists then looked at I.Q. scores in 63,951 pairs of brothers, and found the same results. Differences in household environments did not explain elder siblings’ higher scores.

Because sex has little effect on I.Q. scores, the results almost certainly apply to females as well....

To test whether the difference could be due to biological factors, the researchers examined the scores of young men who became the eldest in the household after an older sibling had died. Their scores came out the same, on average, as those of biological firstborns.

“This is quite firm evidence that the biological explanation is not true,” Dr. Kristensen said in a telephone interview.

Social scientists have proposed several theories to explain how birth order might affect intelligence scores. Firstborns have their parents’ undivided attention as infants, and even if that attention is later divided evenly with a sibling or more, it means that over time they will have more cumulative adult attention, in theory enriching their vocabulary and reasoning abilities.

But this argument does not explain a consistent finding in children under 12: among these youngsters, later-born siblings actually tend to outscore the eldest on I.Q. tests. Researchers theorize that this precociousness may reflect how new children alter the family’s overall intellectual resource pool.

Adding a young child may, in a sense, diminish the family’s overall intellectual environment, as far as an older sibling is concerned; yet the younger sibling benefits from the maturity of both the parents and the older brother or sister. This dynamic may quickly cancel and reverse the head start the older child received from his parents.

Still, the question remains: How do the elders sneak back to the head of the class?

One possibility, proposed by the psychologist Robert Zajonc, is that older siblings consolidate and organize their knowledge in their natural roles as tutors to junior. These lessons, in short, benefit the teacher more than the student.

Another potential explanation concerns how siblings find a niche in the family. Some studies find that both the older and younger siblings tend to describe the firstborn as more disciplined, responsible, high-achieving. Studies suggest — and parents know from experience — that to distinguish themselves, younger siblings often develop other skills, like social charm, a good curveball, mastery of the electric bass, acting skills.

“Like Darwin’s finches, they are eking out alternative ways of deriving the maximum benefit out of the environment, and not directly competing for the same resources as the eldest,” Dr. Sulloway said. “They are developing diverse interests and expertise that the I.Q. tests do not measure.” [As one of four siblings I can tell you that niche partitioning is real.]

This kind of experimentation might explain evidence [ed.: but see below] that younger siblings often live more adventurous lives than their older brother or sister. They are more likely to participate in dangerous sports than eldest children, and more likely to travel to exotic places, studies find. They tend to be less conventional than firstborns, and some of the most provocative and influential figures in science spent their childhoods in the shadow of an older brother or sister (or two or three or four).

Charles Darwin, author of the revolutionary “Origin of Species,” was the fifth of six children. Nicolaus Copernicus, the Polish-born astronomer who determined that the sun, not the earth, was the center of the planetary system, grew up the youngest of four. The mathematician and philosopher René Descartes, the youngest of three, was a key figure in the scientific revolution that began in the 16th century.

Firstborns have won more Nobel Prizes in science than younger siblings, but often by advancing current understanding, rather than overturning it.

Years ago, at a NAAR scientific advisory board meeting, one of the scientists - worked on dyslexia - told me that a very famous researcher had a practice of routinely threatening to sue any scholar who criticized his data or his results.

He had basically shut down the entire peer review process by means of private legal threats.

This researcher receives constant publicity; he seems to be on numerous reporters' Expert list - he's the person called first for comment.

Write a short explanation of why the slope formula works, and include an explanation of why either point can be point 1 or point 2.

The solution manual simply refers you back to the Lesson, which doesn't "explain" why the slope formula works.

I said that the slope formula "works" because slope is "defined" as change in y coordinate divided by change in x coordinate.

However, I can't explain why it doesn't matter which point you designate as point 1. The best I could come up with was something along the lines of...."subtraction is defined as addition of the opposite".... and I'm not even sure that's relevant, to tell the truth.

from Tracy:

I assume the formula you are using for the slope of a line is

(y1-y2)/(x1-x2)

It doesn't matter whether you chose point 1 or point 2 because if the slope is positive and you chose a lower point as point 1 and do the subtractions you wind up with a negative number on top and a negative number below the divsor line, and a negative number divided by a negative number is a positive number.

If the slope is negative, then you wind up with one positive number and one negative number regardless of what you pick as point 1 so the result of the divison is a negative number.

from Greta

When you switch the two points, the sign in each difference changes but the absolute value remains the same: X1 - X2 is the opposite of X2 - X1, and Y1 - Y2 is the opposite of Y2 - Y1. The absolute value of the quotient (the difference in Y divided by the difference in X) will not change since the absolute values of the two differences don't change. The sign of the quotient will not change either: If you had two positive differences before, you will end up with two negative differences after switching the points; either way, the quotient is positive. (Same result if you started with two negative differences.) If you had one negative and one positive difference before (negative quotient), each sign will switch, and you will still have one negative and one positive difference, resulting in a negative quotient.

from Steve H:

(y1-y2)/(x1-x2)

= -(y2-y1)/[-(x2-x1)]

= -1*(y2-y1)/[-1*(x2-x1)]

= -1/-1 * (y2-y1)/(x2-x1)

= (y2-y1)/(x2-x1)

I really appreciate this.

I "know" why you can use either point as "Point 1," but I have no idea how to express it....which leads me to my next plea for help.

Monday, June 25, 2007

One of the most elegant, most influential and most groaned-about pieces of software in the history of computers is 20 years old. There won't be a lot of birthday celebrations for PowerPoint; the program is one the world loves to mock almost as much as it loves to use.

While PowerPoint has served as the metronome for countless crisp presentations, it has also allowed an endless expanse of dimwit ideas to be dressed up with graphical respectability. And not just in conference rooms, but also in the likes of sixth-grade book reports and at PowerPointSermons.com.

As it happens, what might be called the downside of the culture of PowerPoint is something that bemuses, concerns and occasionally appalls PowerPoint's two creators as much as it does everyone else.

Robert Gaskins was the visionary entrepreneur who in the mid-1980s realized that the huge but largely invisible market for preparing business slides was a perfect match for the coming generation of graphics-oriented computers. Scores of venture capitalists disagreed, insisting that text-based DOS machines would never go away.

With major programming done by Dennis Austin, an old chum, PowerPoint 1.0 for Macs came out in 1987. Later that year, Microsoft bought the company for $14 million, its first acquisition, and three years later a Windows version followed.

Gaskins and Mr. Austin, now 63 and 60, respectively, reflected on PowerPoint's creation and its current omnipresence in an interview last week. They are intensely proud of their technical and strategic successes. But to a striking degree, they aren't the least bit defensive about the criticisms routinely heard of PowerPoint. In fact, the best single source of PowerPoint commentary, both pro and con, (including a rich vein of Dilbert cartoons) can be found at RobertGaskins.com, his personal home page.

Perhaps the most scathing criticism comes from the Yale graphics guru Edward Tufte, who says the software "elevates format over content, betraying an attitude of commercialism that turns everything into a sales pitch." He even suggested PowerPoint played a role in the Columbia shuttle disaster, as some vital technical news was buried in an otherwise upbeat slide.

No quarrel from Mr. Gaskins: "All the things Tufte says are absolutely true. People often make very bad use of PowerPoint."

Mr. Gaskins reminds his questioner that a PowerPoint presentation was never supposed to be the entire proposal, just a quick summary of something longer and better thought out. He cites as an example his original business plan for the program: 53 densely argued pages long. The dozen or so slides that accompanied it were but the highlights.

Since then, he complains, "a lot of people in business have given up writing the documents. They just write the presentations, which are summaries without the detail, without the backup. A lot of people don't like the intellectual rigor of actually doing the work."

One of the problems, the men say, is that with PowerPoint now bundled with Office, vastly more people have access to the program than the relatively small group of salespeople for which is was intended. When video projectors became small and cheap, just about every room on earth became PowerPoint-ready.

Now grade-school children turn in book reports via PowerPoint. The men call that an abomination. Children, they emphatically agree, need to think and write in complete paragraphs.

Christopher was given a PowerPoint assignment this year in social studies. Next year, at the end of 8th grade, the kids can do one of two projects for their big ELA assignment:

I went to their Open House with a friend to hear the pitch, and they made us sit through a whole, long PowerPoint prsentation their 5th grade class had done.

That was it.

PowerPoint

A PowerPoint presentation made by other people's children. Ed had to tie me down to get me to watch my own kid's PowerPoint presentation; why would I want to watch anyone else's kid's PowerPoint presentation?

I'm off to Singapore next week for a summer math program and will add these questions to my growing list. We'll get to observe and discuss at two primary schools, one secondary and the National Institute of Education

Are there any other questions about Singapore math curriculum and implementation you would like answered?

Autism researchers are only beginning to assemble a wealth of observational details into a coherent theory of what causes autism.

Different subsets of these observations can evoke competing testable hypotheses (which are healthy for science) and competing ideologies (which are not).

As your article notes, the vaccine idea has been epidemiologically tested and not borne out. It seems time to move on.

I worry, though, that this vaccine controversy has steered the field away from environmental causes in general. As a brother and uncle to two people with autism, I am keenly aware of the role of genetics. But genes can affect responses to the environment, and the environment can influence gene expression, making the genetic-environmental dichotomy a false one.

One truth our work has taught us is that the perturbations of brain development that lead to autism are usually the product of multiple interacting causes. Surely autism research has room for all of these, and for all of us.

Matthew BelmonteIthaca, N.Y., June 18, 2007

The writer is an assistant professor of human development at Cornell University.

Ed says this is the clearest and most succinct statement of the relationship between genes and environment he's seen.

I teach a class at the college level for first semester freshmen. It's intentionally designed as a process course and is targeted at students who think they want to major in business. However, students have to accumulate a certain GPA with a certain number of credit hours before they are admitted to the College of Business (COB). In the meantime, they are taking gen ed courses, and other required courses that serve as prerequisites, such as the managerial and financial accounting classes.

The course itself has multiple goals: we want to introduce them to the standards and expectations that the COB has for its students, we want to cover each of the substantative areas involved (accounting, finance, insurance, management, technology, marketing, international business, ethics, etc.), so that the students have an understanding of what a business degree involves, and we want to introduce them to the Career Center and get them started thinking about what job opportunities might be available with certain majors and the steps that they need to be taking to make their goals become a reality.

With first semester freshmen, I also talk with them quite a bit about the expectations of professors and how college is not the same as high school. For example, professors actually expect that students will read the Syllabus.

Some students are going through a tremendous adjustment. For almost all of them, they are on their own for the first time: mom (or dad) isn't there to get them up in the morning and make sure they get to class, and mom's not there to nag them to get to bed on time and to eat healthily and to remember to exercise.

For some, this freedom is overwhelming, and quite frankly, some of them have to learn some painful lessons the hard way. I always talk to them about how hard it is to dig out of a hole of a lousy first semester GPA. Some students don't have good study habits; some just aren't interested. Most of them admit to being procrastinators; it's just that they aren't very effective at it. It takes a lot of practice and skill to become good at procrastination.

I also ask them to think about and focus on why they are at college; what are their expectations, why are they here, etc. Quite frankly, some of them have no idea; it was just the next step after high school. Others are quite focused and know exactly what they want to accomplish.

I also talk with them about the accounting and finance courses. These courses are tough courses substantively. Accounting is cumulative; most students need to do the homework on a daily basis, and actually start studying well before the first test. And, if they don't do well on the first test, the outlook isn't good for the remainder of the semester (without significant changes) because they don't have the foundation in place. It may be seen as a "gatekeeper" class, but there are reasons for that. Accounting is the language of business, and if students can't gain minimal proficiency, we're not willing to rubber stamp their diploma.

Separate and apart from the "survival" issues (and yet intertwined as well) are whether the students have sufficient background knowledge in the first place. I require my first year students to do a lot of writing; the assignments are varied in length and have multiple purposes. I spend a lot of time at the beginning of the semester making sure that they fully understand what my expectations are in that regard. You don't want to staple your paper? Fine, but after a grace period, you are going to lose points. You don't use complete sentences? You will lose points. However, I go to great pains to follow my procedures, and part of that process includes a lot of what I will call direct teaching, with lots of examples.

To be frank, some (perhaps most) students catch on pretty quick. Others don't, for a variety of reasons. But the bottom line, and I tell them this, is that I want them to succeed.

job placement after college

Catherine again: Slightly off-topic, I have a question about business majors.

What might explain the positive effects of higher grading standards? One possibility is that parents may devote more attention to their children’s schoolwork if their grades suggest that they are struggling.

I teach General Chemistry at a small, moderately selective liberal arts college. We provide a lot of support, but still every year have students flunk out. Often they have decent test scores and grades (in fact, the students who are accepted on probation almost never flunk out). Those who do get sent home often simply refuse to do any work. I have almost begged students to get me something that I can grade, including one person's senior thesis! (And at a big place, those students are just going to be allowed to disappear).

You also do need to be careful in comparing graduation rates -- ours aren't great, but most are students who choose to leave, often to save money or for a different social scene.

By the by, we do see helicopter parents, but these aren't parents with normal concerns. It is the person who calls me to ask when his daughter's final exams will be, or the person who calls an advisor asking where her child is right this minute. In other words, people who contact the professor when they should talk to their kid.

Very interesting.

I find this so strange.

I've never heard such a thing (in real life, that is).

I'm curious whether these parents act apologetic for calling -- ?

That is, do they act as if they know this is an unusual call or request?

another question

I'm also curious about students who go to college and don't do the work.

Is this happening more often today than it used to?

I've mentioned before that I think I'm seeing more kids come back home during freshman year than I did when I was 18. Maybe that's not the case, but it sure seems like it.

I don't remember anyone at Wellesley leaving in the middle of freshman year.

I may have to force my friend P. to hand over her son for part of the summer. He has a natural interest in math, but is now being potentially moved down to the SPED math track because he can't do word problems.

I'm pretty sure I can fix that.

the Skill Builders series

These little books cost $2.95 apiece.

They can be a bit difficult to track down, so I've got their ISBN numbers here:

Parents are paying customers, not helicopters. The college should teach and the parents should parent. For the astronomical amounts that colleges charge, they should not expect parents to pay the bill and go away.

Little (big) Johnnie or Suzie might drop out after $40,000+ is spent with absolutely nothing to show for it. The presumption that the onus falls completely on the student is a cop-out. Johnnie or Suzie might deserve to flunk out, or it could be that the school takes their money and tosses them into the deep end of the pool.

Many parents would be more than happy to let their kids figure it out on their own after they hit 18, but not when it's costing them $40,000+ a year. And colleges should worry more about their flunk-out rate after a highly competitive application process. [ed.: exactly]

Most colleges aren't lowering their standards to recruit students. They get to pick the best for their school. Then they demand extraordinary amounts of money to teach the kids in a sink or swim environment. Then they want the parents to pay the bills and go away.

It won't happen. The problem isn't about growing up, it's about getting something for your money.

We know a family whose child may not make it through college; I believe the parent is in debt for at least $40,000.* Middle class income. When we look at colleges I'm going to want to know a school's college completion rate and success rate at placement in graduate programs. I don't want to pay $40,000 (make that borrow $40,000) for gatekeeping.

Paying $22,000/yr for gatekeeping in my middle & high school will be quite enough.

We've also been told that Cornell's entry-level science courses are particularly brutal. You send your science kid to Cornell, and by second semester freshman year he's majoring in sociology.

Ed says NYU has a fantastic record getting its undergraduates into graduate programs, fyi. That's good to hear. Our big perk in life is that C. can attend NYU for free if he's accepted. We pay taxes on the tuition fee, but that's it.

On the other hand, although I've thought the helicopter parent meme was a crock ever since I heard the words, last weekend my sister-in-law, a professor in a nursing program, told me she has parents calling her up constantly to tell her their child is sick and can't come to clinic; can she give them a do-over; etc.

I find that bizarre.

Ed says he's never heard from a parent in his entire career. Of course, he did once hear from a psychiatrist that one of his students wanted to murder him along with a couple of other professors. (That's another story.)

His brother said Bryn Mawr hears from parents, but I have no sympathy for Bryn Mawr given what it's charging. Of course if parents are calling their kids in sick, my feeling is the kid better be in the hospital even with the $40,000 bill.

sheesh

accountability at the graduate level

Interestingly, graduate-level programs probably have quite a bit of accountability.

Ed is the head of the Institute of French Studies, which awards Ph.D.s. The university closely tracks placement of their graduates in assistant professorships. One year the statistics got messed up so it looked as if they hadn't placed their new Ph.Ds in jobs, and Ed heard from the administration right away.

I'm going to try to get him to look into what kinds of accountability exists for undergraduate education in general.

accountability in schools of design

Gosh, I wish I could remember the conversation Ed had with our friend who is an architect on the Ground Zero buildings....

He was talking about the point at which gatekeeping should begin.

I think he said that in the field of design, professor-as-gatekeeper should start in early graduate school. Assuming I'm remembering this correctly, I believe he said that by then a professor in a good school of design can easily distinguish different levels of talent and accomplishment, and that the job market in design is so competitive that it is an absolute waste of money to pusue an advanced degree in design if your professors don't think you can make it.

It's possible he said this about undergraduate programs like RISD's, but I don't think so. I have the distinct impression he put the gatekeeping function pretty far down the line. I definitely recall finding what he said both useful and commonsensical. It made sense to me both as a person who once attended graduate school and as a person who may one day be trying to pay for graduate school.

In any case, I dislike surrogate gatekeeping. Medical schools don't need Cornell to help them winnow out applicants.

speaking of medical schools

One of our administrators is friends with a high-level administrator at a medical school. (I think the friend may be a dean.)

He said that across the board the best colleges produce students with the best standardized test scores. This is true without fail.

None of this stuff is a mystery.

And no medical school needs undergraduate institutions to make their choices for them.

*In this case the problem is almost certainly that the student simply is not prepared for college level work. Of course, this raises the question of whether the college should be taking the parent's money, and I don't know the answer to that since I don't know what the student's scores and grades were.